Acoustic attenuator for air impellers



y 1943- E. H. HARRIS 2,323,394

ACOUSTIC ATTENUATOR FOR AIR IMPELLERS Filed March 14 1940 3 Sheets-Sheet 1 FIG. 2

July 6, 1943. E. H. HARRIS 2,323,394

ACOUSTIC ATTENUATOR FOR AIR IMPELLERS Filed March 14, 1940 3 Sheets-Sheet 2 FIG 4 f July 6, 1943.- 5. H. HARRIS 2,323,394

ACOUSTIC ATTENUATQR FOR AIR IMPELLERS Filed March 14, 1940 3 Sheets-Sheet 3 INVENT OR Patented July 6, 1943 ACOUSTIC ATTENUATOR FOR AIR IMPELLERS Eliot Huntington Harris, New York, N. Y.

Application March 14, 1940, Serial No. 323,938

2 Claims.

My invention relates to a device for attenuating the sounds incident to the rapid rotation of impellers immersed in a fluid medium.

The device constituting the subject matter of my invention is adaptable for aeronautic propellers, ventilating fans, marine propellers, special types of impellers such as the enclosed blade and slotted disc types operating in a fluid medium.

My invention, briefly stated, resides in the disposition about a rotatable impeller of an annuloid enclosure, in circumferential relationship to said impeller, the inner boundaries of said annuloid enclosure so disposed with respect to said impeller as to prescribe or define a zone or port for intake, and a zone or port for the discharge of the fluid and thus partaking of the nature of a nozzle and which, for the sake of brevity, will hereinafter be referred to as a nozzle.

Within said annuloid enclosure there are disposed a multiplicity of acoustic reflector pipes having access to the space circumscribed by the nozzle through apertures that allow passage of acoustic waves from said'circumscribed space to within said reflector pipes and passage outward These reflector pipes are of of return waves. such size and shape as to serve to reduce the amplitude of the sounds of such frequency as it is desired to attenuate.

The primary object of my invention is to attenuate those sounds from a rotating impeller that have the greatest intensity together with a great carrying power, or power of propagation. A further object is to provide a sonic attenuator in such form that it will result in the least amount of drag due to the resistance of the fluid in which the attenuator is immersed. Further objects will be disclosed as the description progresses.

In the accompanying drawings, illustrating different embodiments of my invention:

Fig. 1 shows a front elevation of one half of the annuloid attenuator which is circumscribed about a rotatable impeller;

Fig. 2 shows, in plan view, a cross-section of an annuloid attenuator, made on the plane of the coincident axis of the impeller and annuloid;

Fig. 3 shows, in cross section on line 3-3 of Fig. 4, one reflector pipe and two resonators;

Fig. 4 shows, in plan view, one reflector pipe and two resonators;

Fig. 5 shows one of themany strips which may be used to fabricate the interior surface of the annuloid attenuator;

Fig. 6 shows, in plan view, an axial cross-section of another form of annuloid attenuator.

Proceeding to a more detailed description of my invention, and referring to Fig. 1 and Fig. 2 of the drawings, the numeral 1 denotes an attenuator with an interior directing surface, shown in the cross section at 2, placed about the periphery of the circle described by propeller 3 rotating on shaft 4. The exterior surface of annuloid i is indicated by numeral 5 which forms, together with the inner surface 2, the annuloid enclosure. Numeral 6 indicates the openings which pierce the inner surface 2 of nozzle l. Numeral I indicates the reflector pipes shown in detail in another drawing. Numeral 8 indicates the resonators attached to reflector pipes. Numerals 9 iudicate'the structural straps for support of the unattached ends of reflector pipes l. The arrows indicate the direction of air flow within the acoustic duct prescribed by the inner surface 2 in the direction from numerals H] to numerals l I.

Fig. 3 illustrates a reflector pipe I with one end l4 open and the opposite end I5 closed. Adjacent to the closed end [5 are located resonators 8'. The resonators are connected to the interior of the reflector pipe I through oriflees l6.

Fig. 4 illustrates a plan view of a reflector pipe l"..with two resonators 8" at the preferred angular relationship to each other. These resonators, with necks, or orifices 16' located in the same circumference of the reflector pipe 1 are at the least angle to each other that their structural limits allow.

Fig. 5 illustrates one of the many similar strips required to form the inner, curved surface 2 of the nozzle I. The flexible strip l8 has its longest dimension divided into a number of unequal divisions. Distance between successive divisions are a, b, c 9". The width, at the successive divisions, is indicated by a, b, c k. Computations for these dimensions are given in the specifications.

Fig. 6 illustrates a modification of the attenuator shown in Fig. 2. Curved reflector pipes 1" replace the straight pipes shown in Fig. 2 and also the exterior surface 5" is cylindrical except for a slight bell at the down stream edge H".

The numerous factors which have their function in the design of my attenuator will be considered under two headings. First the sonic considerations, and second, the fluid dynamic considerations. The speciflcationswill first describe the design and construction of my attenuator for aeroplane propellers. Modification for other uses will then be indicated.

Considering the sonic factors, it is first necessary to decide upon the particular wave motions to be attenuated. To do this it must be determined whether the purpose of attenuation is to reduce the noise Within the planes cabin or to prevent detection from the ground. For the former consideration, frequencies all within the audible range, from 90 to 8,000 per second, should be investigated. The reason for this choice will be obvious on inspection of a curve showing the threshold of audibility plotted with frequencies and intensities as coordinates. If the plane is to be protected against detection from the ground, the lower frequencies of 80 to 300 should be investigated. By investigation is meant the use of some method to determine the dominant frequencies within the specified range. This investigation may be made by a wide variety of means, such as the use of commercial frequency analysers in conjunction with intensity indicators or perhaps the more simple devices, such as a series of Helmholtz, or variable volume, resonators. By far the best and the preferred method of investigation is to obtain a graph of the sound produced. Such a device as the phonodike may be used for this purpose. The resulting curve should then be analyzed by resolving the complex curve into a series, or group, of sinusoidal waves, as may be done by use of the Fourier theorem. From the result obtained, those frequencies having an important amplitude will be clearly indicated. It should be pointed out that if the purpose is to reduce cabin noise the reading should be taken in the cabin, and if for preventing land detection the reading should be taken from the ground while the plane is in flight at a proper distance and under conditions at which detection will be attempted, allowance always being made for the Doppler effect. The propagation of sonic waves varies considerably with different frequencies, atmospheric conditions, and many other factors such as ground contour, cabin curvature, medium of transmission, etc. Both experimental and theoretical information on sonic wave propagation are available in profusion to those familiar with the sonic arts and should be appreciated prior to the investigation for dominant frequencies. The next consideration, in order properly to design the attenuating device, is the determination of the principal source of the dminant frequencies found. Although not widely published, it is known and may easily be determined that the low frequency sounds, which will be found to be a function of the angular velocity times the number of blades of the propeller in question, will issue most particularly from the blade tips. Blade flecture, both lateral and tortional, may produce important amplitudes. Where one of these is of such frequency that it reinforces a harmonic of the fundamental from another source, then that harmonic may be the principal, or perhaps the only, frequency heard. This latter case has been found true only in small units, such as ventilating fans.

The principal method employed for attenuation of the sonic waves in my device is that of interference. Obviously diffusion cannot be applied and impedance has not been developed for a unit where radial reflection is obtained to the degree present in the device under consideration. Friction, while helpful, will not accomplish sufficient attenuation to warrant construction of a device for its use. Therefore a superimposed wave, having the proper phase relationship to the incident wave, is employed. This may be stated as follows, where the equation expresses the fundamental sinusoidal wave and the consideration is for longitudinal motion of sound. Then:

and

where the expression of y is the incident wave and y the superimposed or reflected wave. g =the dependent variable of amplitude at any point of the vibration. a=the maximum wave excursion, or amplitude. t=the independent variable of time from the datum. T=the time for one wave cycle. a3=the independent variable of distance along the path of wave motion. x=the length of one wave. Then, if these waves are superimposed they will have the same direction and therefore the same sign before the variable of lag. The consideration is of a superimposed wave having the same frequency as the incident wave, thus imposing the same value for T and T If the two equations are added and the expansion is carried out the form will become Now if the proper phase angle is obtained, maximum interference will be had. Assume this to be 1r. Then E"'ZJ: 2

Substituting and reducing, the equation becomes:

21d 2:l;k I y-l-y-a sin T COS1r as an (L OS T Slll'n" A ablll T COS 21d 21rd:

a cos T sin T Examination will show that one of the trigonometrical functions of either the first or second term belonging to each of the original equations will become zero. For example, solve for any point such as and it will be seen that the first and third terms in the above drop out because equal because their limits are the same by definition and their variation was specified to be according to the phase difference of 1r radians. S0, considering ,theminimum and maximum values as the function varies from zero to one, the ,numerical value of y'+y may vary, from to a'a or y'+y=;+:(aa) and the'amplitude of the superimposed wave should be as nearyto that,

of the incident wave as possible for greatestate tenuation.

The next objective is to obtain this superimposed wave.

This may be accomplished for conditions where the wave of dominant frequency issues principally from the blade tip by use of reflector pipes I placed within the annuloid so that their open ends M will be directly in the plane of rotation of the blade tips. If such reflector pipes could form a continuous ring about the propeller, better results would be obtained. Due to space conditions it was found that a greater number of reflector pipes I could be installed if two rows were employed, each having their open ends I 4 0.00129. The velocity for any temperature, t, is:'

Vt=Vu /1+pt where V0 is the velocity at standard conditions and c is the gas expansion coefficient, or 1/273 for air for the c. g. s. system followed here. Another form may be used, viz:

where Pt is the absolute pressure; 7 is the ratio of specific heats and Dt is the density at temperature t, where Dt=DoX( 1+Bt) The velocity for the conditions'un'der consideration will then be assumed as V. The length of the wave in question, A, will then be VX117 where nis the frequency. The pipe length, L,fr0m the, reflector surface at the closed end of pipe to the open end,

pipes must have an equivalent ratio of 12 or more for effective vibration. On the opposite extreme, for ratios of 1 or less, it will be found that dia-,

metrical resonance will predominate and the re-.

fle'ctor value will not be obtained. Thus, the diameter of the reflector pipe is specified within the limits of the ratios given. Construction considerations, may govern within these limits. 'However, each design must be checked to assure that its natural frequency is well outside the frequency to be attenuated. e

To reinforce the fundamental frequency resonators are shown in the drawings although they are "not always necessary. For large units, such as for aviation the resonators are desirable. A.

sharp resonator obviously will tend; to main a n the vibration in the pipev of the frequency for which it is designed. Also the resonator will upset the vibration of the column of air within the pipe due to added volume and the separate resonator effect. The design of these resonators for the frequency, n, is independent of the shape, provided no dimension is large compared to the wave length. The fundamental, mechanical formula for a vibrating member is:

where m mass and k=restoring force per unit displacement. In order to apply this formula to a resonator it must be assumed that all the mass is in the cavity, and restoring force, or elasticity, is in the neck where the hydrostatic effect of increased particle motion 'is obtained. The study of acoustics shows these to be permissible assumptions. By substituting length, area and density for mass, desirable units are obtained for the formula. Considering that the time for any one expansion or contraction does not allow for dissipation of the heat, thus giving an adiabatic condition, it may be shown that:

where 'y=the ratio of specific heat at constant pressure to specific heat at constant volume; p=the pressure variation resulting from the movement; of the vibration particle; A=the area and S=the volume. Substituting i :I 2 1r L but Where V is the velocity of sound. Furthermore, in a thin plate orifice such as those used in the resonators for my device, the length, L, approaches zero, thus A/L may be considered as the diameter of the orifice, designated by D, and the formula becomes K E n 21r S This is similar to the usual form of 1 n 21q/E where L and C are the inertance and capacitance respectively. Using the former convenient form it will be seen that S=(DV x41r n All values on the right hand side of the equation are known with the exception of D which must be chosen. Within certain limits, the smaller the diameter of the orifice, the sharper the resonance and also the smaller the volume of the resonator. However, this diameter must be determined on the basis of the space available, the size of the reflector pipe and a study of the resolved curves. The proximity of the frequency of two or more waves having amplitudes important to the consideration, must be considered in the light of the sharpness desired. Also the orifice should not be reduced to the point of restriction of the reinforcing efiect of the resonator. Obviously where two or more resonators are open into one pipe, they should. all have identical frequencies. If resonators are to be used, it has been found desirable to use at least two. More should be used where space conditions allow. Relative position of resonators was stated previously.

Coupled, or series, resonators have been found to give less satisfactory results than the preferred design shown in the drawings. Coupled resonators will resound to the widest range of frequencies, thus giving an amplitude-frequency curve with overlapping peaks. This obviously is counter to the desired conditions and would result in sonic confusion and occasionally a reinforcing of some incident waves.

The number of reflector pipes employed in any one circle around the interior of the nozzle should be as great as structural conditions permit. If there are two dominant frequencies to be attenuated, alternate reflector pipes in the same circular row should be designed for frequency of the secand dominant amplitude. The same specification should apply to other rows of reflector pipes.

The inclusion of the reflector pipes in the leading edge of the annuloid enclosure, or in other Words the reflector pipes with open ends toward I the suction stream, are effective only where there are clearly defined dominant frequencies at the recording or listening point. Such a condition is had when diffusion dissipates, or attenuates, the high frequencies, leaving the lower frequencies as the audible sound propagated by the propeller. A slight benefit is then obtained from the use of these leading edge pipes.

The reflector pipes with open ends directed rearward, in the direction of the discharge of the propeller, are of importance. The reflection of the sound from the structure, as, for example, the motor housing, will tend to give greater intensity of sound on the face of the propeller opposite the prime mover. In aviation this is the suction side. However, these reflected waves may,

occur in such phase relation as to reinforce or to attenuate the frequency of greatest magnitude of the considered wave motions. Physical measurements wi11 establish this and the location of these reflector pipes can then be established to obtain an attenuating effect in the obvious manner.

The formu ae and constants necessary for the computation of the acoustic features have been given above, together with some explanation of the derivation or the general form of equation, in order that persons skilled in the art of hydrodynamics may visualize the meaning of the acoustic functions involved. computation for coupling of resonators. The equation is given here without explanation as it has application only for unusual circumstances such as ventilating fans issuing high frequency sounds.

N=coup1ed frequency M combined mass m=frequency of resonator #1 n2=frequency of resonator #2 m1=mass of resonator #1 m2=mass of resonator #2 The fluid dynamic consideration of my device is given in general terms, assuming a familiarity i Exception is the with the art by those desirous of constructing my attenuator. The important feature is that of resistance or drag of the annuloid in the fluid in which it is immersed. It is well known that the.

pressure conditions about a rotating propeller arc such that a negative pressure exists at all points to the suction. sideof the plane of rotation. The

discharge side of this plane contains both negative and positivepressures. Negative pressures exist about the blade tips and extend to a varying distance in the direction of the propeller axis. A region of turbulence occurs between the well defined negative and positive positions. The extent and location of this region of turbulence varies with the design of the propeller; magnitude of pressure differential, and the velocity and character of the surrounding fluid relative to the propeller. If a cross-section of the discharge stream-in a plane of the axis of the propeller is considered, the boundary of this discharge stream will follow approximately a parabola curve whose ,focus is adjacent to the blade tip, and the divergent extension of the curve will approach the propeller axis. This is the ideal curve and only the interference by the turbulent region disturbs the preferred functioning of this discharge stream. The suction stream, on the contrary, presents a very unsatisfactory picture. Under many operating conditions there are actually vectors which oppose the desired thrust on an aeroplane propeller. The reverse vectors in the suction stream occur on the discharge side of the plane of propeller rotation. Thus it is correct to say that the suction coefficient is extremely low. A suction nozzle will correct these vector conditions and can be designed to show a coefficient of 0.99. The shape of the nozzle may take many forms of exponential type, but tests with very low differential pressures tend to show that a parabolic outline curve is advantageous for the nozzle. The preferred design of the cross section of my nozzle, as indicated at 2 in Fig. 2, both for suction and discharge, is parabolic.

To determine the change in the combined coeflicient when a nozzle is employed, a reading of the thrust may be taken. When immersed in still air a gain, due to installation of the nozzle, of 20.8% in thrust was the minimum recorded. This is an indication of the improvement in the suction and discharge coefficient. Iti important to note here that this gain was a resultant of two general actions. First, there is the. gain due largely to the imposed form of the suction stream. Then there is a reaction due to the drag of the air on the inner face of the nozzle. This reaction is, of course, predicated on the nozzle being mounted integral with the driving motor. In other words, under these conditions the drag of the inner face of the nozzle has been measured and deducted from the gain due to prescribing the form of flow stream. This consideration is important as it dictates the desired form of the exterior surface of the nozzle. Obviously, drag of the exterior surfac only must be deducted if there is a velocity of the nozzle relative to the fluid in which it is immersed. This surface may then be considered as a thin plate and the drag approximately computed in this manner. To further implement this point it may be explained that if the drag of the nozzle alone i experimentally measured and the gain in thrust by the rotating propeller is also measured, taking care in this case to support the nozzle independently from the propeller and its prime mover, the combined result will be fictitious. In other words, the drag of the nozzle due to the fluid moved by virtue of the propeller rotation, i. e. the drag due to the greater velocity on the interior surface of the nozzle, is integral with the combined coefiicient for that nozzle and must be so considered. Thus'it might be said, without too great exaggeration, that this bulky annuloid ha the 2,323,394 aerodynamic form of a thin plate of cylindrical j the annuloid will be designed for minimum drag without reference to the thickness of the annuloid and, in fact, without reference to any other surface but as'a free and independent surface.

The physical measurement of'length etc. must be considered, but the form chosen within these limits will b governed by the above.

When the increase in thrust is measured under {conditions 'of there being a velocity of the surrounding fluid relative to'the nozzle, p opeller and motor, the gain obviously will vary with the numericalfvalue. of this velocity, other conditions remaining the same. The result of such examinationshows a positive gain in thrust over a wide variety of conditions. The increase in thrust, determined by measurement of the thrust of th rotating propeller first without any nozzle and then with my annuloid attenuator installed, the power input being constant, varied from 0.4% to 12.8%, according to velocity conditions tested. The above indicates the choice of flat plate construction for the exterior surface of the annulold.

The controlling dimensions of the nozzle are the necessary physical requirement rather than the fluid dynamics. Thus the length of th reflector pipe will determine the length of the base line of the exponential outline curve of the nozzle. While these pipes may be curved, it is preferred to have them in straight cylindrical or rectilineal form.

The discharge section of my nozzle should have an outline curvature of the exponential type and the preferred design is parabolic. The form of this curvature may be as shown in Fig. 2 of the drawings, or it may be of such form a to increase the discharge velocity by creating a reduction of area at the vena contracta. This latter design will require a double curvature outline. For a given rotational speed and pitch of any one propeller the momentum may be shown to vary rirectly as the velocity and therefore inversely as the area of the vena contracta of the nozzle. This feature is not an essential of my device but it offers a series of combinations useful to the aerodynamic engineer and is inherently a function of the nozzle.

The structural material of my device may be steel, aluminum, or other suitable substance. The form of the annuloid provides good structural strength and therefore may be constructed of very l ght plates exceptat the section of the inner surface adjacent to the propeller tips where reinforcing is required. Th inside face of the nozzle 2 should be so treated as to reduce the acoustic reflection. Any standard material may be employed, such as the asbestos coated metal. One method of forming the convergent divergent curved nozzle is indicated in Fig. 3. This method is to construct the curved surface from a number of flat strips. Thus if the complete circle is divided into 20 parts, each section will be a chord of an 18 angle. The axial length of the nozzle should be divided into a number of equal parts and the diameter of the inner surface at each of these equal divisions obtained by computations from the formula of the curve. Thus, if a parabola is employed, the constant q may be determined by solving the formula z=q i l some point whereboth r andy are known. For example, where y=0L57 times the axial length of the nozzle, 1: Will be /2 the base of the parabola or /2 the double ordinate which forms this base. As stated vabove,this base is determined by the length of the reflector pipe plu clearance. I have assumed here that th zero ordinate line, or axis, of theparabola passes through the apex of the curve, rather than complicate thecalculations by the additive constant necessary to havethe said ordinate line coincide with axis of the nozzle.

Thus the length of the reflector pipe plus the thickness of materials employed plus tolerances will'equal o'ne-half'the base, or equal .r for a value of y as above. It may be specified here that the interior face of the nozzle 2 of Fig. l, is cylindrical, for a short distance, about the plane of propellerrotation, usually for 6% of the axial length of the nozzle. Therefore the figure 0.57 times the axial length of the nozzle is the maximum value of y for the suction curve shown in the drawings. Having determined the value of the constant, q, as above, the value for :0 may be determined for the chosen values of y, where 1/ is the distance from the leading edge of the nozzle; i. e., the apex of the outline curve. The radius of the .circle which would be described by the intersection of a plane normal to the propeller axis and the inner surface of the nozzle, for each value of y chosen is found by subtracting the value of x from the sum of the propeller radius plus the clearance plus /2 the base of the parabola. This sum may otherwise be stated as equal to the radius of the nozzle at it leading I edge where a; and y equal zero. Each chord subtended by the 18 angle will be the computed radius, or radius of the inner surface of the nozzle for each value of 11, times twice the sine of /2 the angle, or chord=r2 sin /20. The actual length along the curve between the successive values of 11 may be found by the integral 'W y!) 2 96 t [(a) v where y and 11" represent two points along the y axis, where the derivative of a: with respect to 11/ must be found in terms of 11. Thus th widths of the strip in Fig. 3, viz: a, b, 0, etc. are the chords, as above, and the unequal distances between these measurements, viz: a, b, 0', etc. are the arcs, S, as above for the chosen equidistances of y. Similar calculations for the curvature of the discharge end of my nozzle will give the dimensions of the strips which, when welded together, will form the desired shape of the nozzle from leading to trailing edge.

The reflector pipes may be constructed of composition board, press board or equal material for this purpose. It is desirable to have the sides and closed ends stiff against vibration. The resonators may be either the preferred, spherical shape or they may be cylindrical. Rectangular shapes are liable to give an undesirable vibration in their flat walls. If this is prevented, as it must be in the case of the closed end of a cylindrical resonator, then fiat wall shapes are adaptable.

The method of mounting need not be considered here except to say that since no practical way of dynamically balancing the annuloid has been conceived, it should be attached to some rigid member and clearance allowed for the rotating propeller.

If the device is to be applied to a marine propeller the resonators should be omitted, and the increased length of the reflectorpipes, due to the high velocity of sound in water, will indicate theuse of curved pipes to avoid an excessive width of the annuioid.

Other requirements, modifications and tolerances will be obvious to those skilled in the art. I do not limit my invention to the constructions herein illustrated and described, such illustrations and descriptions being merely for the purpose of showing how the principles underlying my invention may be carried into practice. Incident wave issuing from other sources than the one described may be attenuated by interference waves set by other series of reflector pipes, with or without resonators, according to the same general specifications.

Iclaim:

1. An acoustic attenuator of the class described comprising an annuloid, the inner face of said annuloid having a divergent curvature from its i.

'fiector pipes within said annuloid having openattenuated, each of said pipes to have an interior length equal to one quarter of the wave length of the sonic frequency to be attenuated minus the distance from open end of said pipes to the source of said sonic frequency, a resonator .for .each of said vpipes having tuned frequency identicalto the .sonic frequency for which said reflector pipeis measured and said resonator acoustically connected to said reflector pipe near .its closed end.

ELIOT HUNTINGTON HARRIS. 

